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矩阵是否可逆的两种。Either the matrix is invertible.

无限维球面可逆吗？Are Infinite Dimensional Spheres Invertible?

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在上一节中，几乎所有的变换都是可逆的。In the previous section, almost all transformations are invertible.

当矩阵可逆和不可逆时，到底是什么情况？So, what happens to these two situations when a is invertible or not?

通过简单的展开运算和加法操作就可实现逆变换。This method is invertible through simple expansion and additional operations.

映射置乱了像素的位置，过程是可逆的。The left map sod the right map shuffle the positions of image pixels which ace invertible.

正交矩阵是可逆矩阵，其逆矩阵等于其转置矩阵。An orthogonal matrix is an invertible matrix for which the inverse is equal to the transpose.

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目的给出算子逆配置及缺项算子矩阵的逆补刻画。Aim To characterize the invertible assignment problem and the invertible completion on operator pairs.

利用拉伸和折叠的原理，提出了一种可逆映射集合的图像加密算法。Utilizing the stretch and fold mechanism, an invertible map set based image encryption algorithm is proposed.

将有界分配格上可逆矩阵的有关结果推广到坡上的矩阵。Some results related to invertible matrices over bounded distributive lattice are generalized to matrices over incline.

并将所得结论应用于可逆线性变换概率空间的性质研究中。Counting formulas are given and applied in the research on properties of invertible linear transformation probability space.

得出了这类线性可逆变换存在对偶性的充分必要条件。Further, in this paper the sufficient and necessary condition for the duality of this linear invertible transform is obtained.

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针对在非线性混叠盲源分离中代价函数往往具有许多局部最优解，求解其全局最优解非常困难的问题。In nonlinear blind source separation, the approach for invertible functions is very difficulty due to the existence of many local minima.

构造了一类符号可逆图，并给出了这类图的符号逆图是平衡图的充要条件。We now construct a class of signed invertible graphs, and obtain the condition of equivalence of their signed inverse graphs′being balanced graphs.

刻画了在非负无零因子交换半环上强保持可逆矩阵的线性算子。The linear operators that strongly preserve invertible matrices over some antinegative commutative semirings with no zero divisors were characterized.

基于线性可逆变换方法，提出一种有效提高延迟反馈法控制混沌的方案。A scheme, which can be used to effectively improve the quality of time_delayed feedback control of chaos, was proposed based on linear invertible transform.

在第二部分中，我们研究了较一般情形下前馈逆有限自动机的结构，并且讨论了弱可逆有限自动机的结构。In the second part, we study the structure of feedforward inverse finite automata in general case, and we also discuss the structure of weakly invertible finite automata.

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有两种可能，一是方程组可逆,这就是一般情况了,这时三个平面交于一点。And then, we have two cases. So, the case where the system is invertible corresponds to the general situation where your three planes somehow all just intersect in one point.

本文证明对低于4维的仿射非线性系统，可通过可逆动态状态反馈线性化的系统一定可通过加积分器线性化。In this paper, we prove that invertible dynamic feedback linearizability is equivalent to linearizability by adding integrators for up to 4 dimensional affine nonlinear systems.